Hausdorff linkage is the twin of Minimax linkage, but much less widely known.
The name obviously comes from Hausdorff distance, a very classical measure for the distance of sets.
The objective is the "maximum minimum distance", i.e., choose the merge $A\cup B$ with the smallest
$$\max\left\{\max{a\in A} \min{b\in B} d(a,b), \max{b\in B} \min{a\in A} d(a,b)\right\}$$ and can be seen as finding the shortest edge such that every point from either set is connected to some point of the other set.
Basalto, Nicolas; Bellotti, Roberto; De Carlo, Francesco; Facchi, Paolo; Pantaleo, Ester; Pascazio, Saverio
Hausdorff clustering of financial time series
Physica A: Statistical Mechanics and Its Applications. 379 (2): 635–644.
Hausdorff linkage is the twin of Minimax linkage, but much less widely known.
The name obviously comes from Hausdorff distance, a very classical measure for the distance of sets.
The objective is the "maximum minimum distance", i.e., choose the merge $A\cup B$ with the smallest $$\max\left\{\max{a\in A} \min{b\in B} d(a,b), \max{b\in B} \min{a\in A} d(a,b)\right\}$$ and can be seen as finding the shortest edge such that every point from either set is connected to some point of the other set.